Quarks have a basic problem: they don't like to be apart. If you try to pull them apart they get upset. As you pull them apart the energy needed to pull them further apart keeps increasing. (this is unlike, say, an electron and a proton, where it decreases). If you pull them too far apart the energy between them is so large that two new quarks can be created (because energy is equivalent to mass). The new quarks will have the right color charge to cancel the color charges of the original quarks, and so they will all be happy again.

The upshot of all this is that quarks have to be bound with other quarks in a composite particle. These are called hadrons. There are two ways a hadron can make the color charges cancel: having two quarks with opposite colors (red/anti-red), in which case the hadron is a meson; or having three quarks, one with each color (red/green/blue), in which case the hadron is a baryon.

The particles that bind the quarks together inside a hadron are called gluons.